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\large{Name:} \hfill    \large{Probability for Scientists, Fall 2013}

\large{Collaborator(s):} \hfill    \large{ Bio 409 / Bio 509 / Stat 479 } 

\hfill    \large{ Lab 1 (35pts), Due 3 Sep 2013 }

\large{You don't need a calculator for this assignment.  Please show your work,
and leave answers as fractions.}

\section{(5) Ask a question:}
Email a question to the class address (probforsci@x14n.org).  The question can
be about this lab, or anything from class or the readings.  The subject of the
email should summarize the question.

\section{(5) Solve for the following:}
    \begin{enumerate}
        \item $\frac{3^4}{2^5}$
        \item $(\frac{2}{3})^4$
        \item $5!$
        \item $\frac{1,000!}{998!}$
        \item $\frac{(10^5)!}{(10^5-1)!}$
    \end{enumerate}


\section{(5) Write the following as fractions:}
    \begin{enumerate}
        \item Nine times out of ten.
        \item Never.
        \item Always.
        \item Even odds.
        \item Once in a blue moon.
    \end{enumerate}


\section{(20) Mating pairs:}
    \begin{enumerate}
        \item A nuclear apocalypse has ravaged the globe leaving 10 surviving pigeons, only 4
of which are capable of reproduction.  What is the probability that at least one
breeding pair of pigeons has survived to repopulate the world?
        ~\\
        ~\\
        ~\\
        ~\\
        ~\\
    
        \item What assumptions did you make to arrive at this probability?
        ~\\
        ~\\
        ~\\

        \item In the above scenario, assume that pigeons have 5 possible sexes
(some fungi, for example, have more than 2 sexes).  Assume that each sex 
was equally abundant before the apocalypse, and equally likely to survive.  Also
assume that members of each sex can mate with any member of a sex other than its
own.  Now what is the probability of at least one breeding pair?
        ~\\
        ~\\
        ~\\
        ~\\
        ~\\
        ~\\

        \item Does this suggest a benefit from having more than 2 sexes?  Can
you think of a scenario where this would be helpful?
    \end{enumerate}

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